Barking up the right tree: binomial option valuation of investments in steel making

A case study of Metals and Polymers*

Master’s thesis presentation 01/06/2012

Author: Dmytro SerebrennikovSupervisor: Luca Di Corato *www.metipol.com

The object of case study: Metals and Polymers Ltd

• Established in 2008• Alchevsk, Eastern Ukraine • Produces galvanized and polymerized steel• Total capacities – 175 000 tons of output annually• Investment capital (pilot stage) – $72 mln

Future decisions (options) depend on market conjuncture:

• Output prices go up: expansion to 300 000 tons• Investment capital (expansion stage) - $65 mln• Output prices fall / risk of expropriation: abandonment• Assets can be sold at $65 mln

The object of case study: Metals and Polymers Ltd

Research questions:

• 1) How will the options to expand and to abandon affect the value of the factory if both of them are implemented separately and together?

• 2) How will the value of the factory and the values of the embedded options change in response to changes in key variables: rate of corporate tax, discount rate and volatility?

Method

• Positivistic approach: the validity of the numerical model used is tested

• Data collection:

- primary info is derived from financial statements

- it is delivered in a pre-structured form suitable for the theoretical model selected (Excel sheet-integrated)

- interview is arranged to make clear contextual details

• Data analysis: Microsoft Excel

Theoretical framework

• Net Present Value (NPV) analysis

• Option valuation model

• Time series analysis

NPV analysis: present value (PV) of a business

FCF – free cash flow n – number of time periods

r – discount rate t – concrete time period

– rate of growth

NPV analysis: Free Cash Flow (post tax cash flow)

Three discount rates are chosen to plug in the model:

1) r = 6,75% - value of a coupon attached to a default-free governmental bond (EUROBOND-2017)

2) r = 9,5% - offered by the firm’s analysts

3) r = 13% - selected arbitrarily to complete the interval

Rate of growth = 3% - rate of drift for polymerized steel

NPV analysis: discount rate (r) and rate of growth ( )

NPV analysis: extended NPV

Option (in real economy ) – an opportunity to change the course of business in response to market signals

Types of options :

• option to expand

• option to abandon

• option to switch

• option to delay

Option valuation theory: origin

Option (financial instrument) – a right, but not an obligation to buy/sell some amount of stock (shares of a company)

Variables comparison

Option valuation theory: origin

Notation Financial option Real option

S Price of stock Market value of assets

K Exercise (strike) price Value of investment capital

t Expiration time Last time to invest in a project

r Discount rate Discount rate

σ Volatility of stock Volatility of output prices

Two-state assumption: price of stock (asset) moves either up or down

Option valuation theory: Binomial lattice (tree)

year 0 year 1 year 2

4)

2) 1) 5)

3)   6)  

Option valuation theory: Value of a call option

year 0 year 1 year 2

4)

2) 1) 5)

3)   6)  

Option valuation theory: Evolution of the asset’s value

Years 0 1 2 3

7 157 №

Asset value Expansion Wait/Abandon

4 135 Item Data Present value 100 Risk-free rate 5.00%

2 116 8 116 (σ volatility) 15% Upside jump (u) 1.161834 Downside jump (d) 0.860708

1 100 5 100 p (probability) 0.628613 1-p 0.371387 Cost of expansion 15.00

3 86 9 86 Expansion factor 1.20 Discount factor 1.05 Selling value 100.00

6 74 Results Options value 11.97

10 64

Option valuation theory: Options to expand and abandon

Years 0 1 2 3

7 157 №

Asset value 173 Expansion Wait/Abandon

4 135 Item Data 147 Present value 100 147.70 Risk-free rate 5.00%

2 116 8 116 (σ volatility) 15% 124 124 Upside jump (u) 1.161834 127.28 Downside jump (d) 0.860708

1 100 5 100 p (probability) 0.628613 104 1-p 0.371387 111.97 109.86 Cost of expansion 15.00

3 86 9 86 Expansion factor 1.20 88 88 Discount factor 1.05 101.14 100 Selling value 100.00

6 74 74 Results 100 Options value 11.97

10 0 Node 5:

Time series analysis: measuring volatility

Evolution of prices for steel products

Jan-9

3

Sep-9

3

May

-94

Jan-9

5

Sep-9

5

May

-96

Jan-9

7

Sep-9

7

May

-98

Jan-9

9

Sep-9

9

May

-00

Jan-0

1

Sep-0

1

May

-02

Jan-0

3

Sep-0

3

May

-04

Jan-0

5

Sep-0

5

May

-06

Jan-0

7

Sep-0

7

May

-08

Jan-0

9

Sep-0

9

May

-10

250

450

650

850

1050

1250

1450

1650

1850

2050

2250

Cold-rolled ($/cwt)Cold-rolled ($/ton)Galvanized ($/ton)Polymerized ($/ton)

Pric

e

Results

• Conventional NPV analysis (no options)

• Extended NPV analysis

The object of case study: Metals and Polymers Ltd

• Established in 2008• Alchevsk, Eastern Ukraine • Produces galvanized and polymerized steel• Total capacities – 175 000 tons of output annually• Investment capital (pilot stage) – $72 mln

Future decisions (options) depend on market conjuncture:

• Output prices go up: expansion to 300 000 tons• Investment capital (expansion stage) - $65 mln• EBITDA will double (expansion factor – 2)• Output prices fall / risk of expropriation: abandonment• Assets can be sold at $65 mln (capital invested in fixed

assets: buildings, transport, equipment)

Conventional NPV analysis (in $ mln)

Base case scenario: tax rate 25%    

 Discount rate 6.75% 9.50% 13%

PV horizon 217,233 97,181 46,116

PV 10 years (observed) 24,537 12,079 - 628

PV total 241,770 109,260 45,488

NPV 169,471 36,961 - 26,811 Scenario lower tax: tax

 rate 20%    

 Discount rate 6.75% 9.50% 13%

PV horizon 235,432 105,322 49,979

PV 10 years (observed) 34,434 20,892 7,067

PV total 269,866 126,214 57,046

NPV 197,567 53,915 - 15,253

Scenario higher tax: tax  rate 30%    

 Discount rate 6.75% 9.50% 13%

PV horizon 199,034 89,040 42,253

PV 10 years (observed) 14,641 3,266 - 8,322

PV total 213,675 92,306 33,930

NPV 141,376 20,007 - 38,369

Extended NPV analysis (lower tax scenario – 20%)

  Discount rate 6.75% Discount rate 9.5% Discount rate 13%Volatility 23% 29.50% 37% 23% 29.50% 37% 23% 29.50% 37%

Present value (PV) 269,865.91 269,865.91 269,865.91 126,214.25 126,214.25 126,214.25 57,046.28 57,046.28 57,046.28

Integrated value 235,829.27 236,544.86 238,882.26 93,459.12 96,836.15 102,107.17 34,354.18 40,029.24 47,566.39

Aggregated value 235,829.27 236,563.82 238,932.44 93,572.39 97,170.99 102,561.62 37,999.69 43,251.71 50,147.08

Expansion option 235,810.78 236,166.99 237,253.57 92,763.39 94,334.47 96,629.96 27,523.77 29,918.04 33,247.21

Abandonment option 18.49 396.83 1,678.87 809.00 2,836.51 5,931.67 10,475.93 13,333.67 16,899.87

Extended PV (expansion) 505,676.70 506,032.90 507,119.48 218,977.65 220,548.73 222,844.21 84,570.05 86,964.32 90,293.50

Extended PV (abandonment) 269,884.40 270,262.75 271,544.78 127,023.25 129,050.77 132,145.92 67,522.21 70,379.96 73,946.15

Extended PV (integrated) 505,695.18 506,410.77 508,748.17 219,673.38 223,050.40 228,321.42 91,400.46 97,075.53 104,612.67

Extended PV (aggregated) 505,695.18 506,429.74 508,798.35 219,786.64 223,385.24 228,775.88 95,045.98 100,298.00 107,193.36

Extended NPV (expansion) 433,377.54 433,733.75 434,820.33 146,678.49 148,249.58 150,545.06 12,270.90 14,665.17 17,994.34

Extended NPV (abandonment) 197,585.25 197,963.59 199,245.63 54,724.10 56,751.61 59,846.77 - 4,776.94 - 1,919.19 1,647.00

Extended NPV (integrated) 433,396.03 434,111.62 436,449.02 147,374.22 150,751.25 156,022.27 19,101.31 24,776.37 32,313.52

Extended NPV (aggregated) 433,396.03 434,130.58 436,499.20 147,487.49 151,086.09 156,476.73 22,746.83 27,998.84 34,894.21

Investments 72,299.15 72,299.15 72,299.15 72,299.15 72,299.15 72,299.15 72,299.15 72,299.15 72,299.15

Major conclusions:

Answer to research question 1:• Introduction of options pumps the project’s value up• The more options are embedded, the higher the value of the

project

Answer to research question 2:

Type of variable Tax rate Discount rate Volatility

Changes in variable Lower Higher Lower Higher Lower Higher

PV of project Increase Decrease Increase Decrease No effect No effect

Value of expansion Increase Decrease Increase Decrease Decrease Increase

Value of abandonment Decrease Increase Decrease Increase Decrease Increase